Transformations 5-6 Learn to transform plane figures using translations, rotations, and reflections.

Transformations 5-6 Vocabulary transformation image translation reflection rotation center of rotation

Transformations 5-6 *A transformation is a change in a figure’s position or size.  Types of transformations: translation, rotation, and reflections The resulting figure, or image, of a translation, rotation, or reflection is congruent to the original figure. A translation slides a figure along a line without turning.

Transformations 5-6

Transformations 5-6 Additional Example 1: Graphing Translations on a Coordinate Plane Graph the translation of triangle ABC 2 units right and 3 units down. Add 2 to the x-coordinate of each vertex, and subtract 3 from the y- coordinate of each vertex. RuleImage A(–3, 4)  A’ (–3 + 2, 4 – 3)A’(–1, 1) B(0, 2)  B’ (0 + 2, 2 – 3)B’(2, –1) C(–2, 1)  C’ (–2 + 2, 1 – 3)C’(0, –2) A’A’ B’B’ C’C’

Transformations 5-6 Check It Out: Example 1 Graph the translation of the quadrilateral ABCD 3 units down and 5 units left. Subtract 5 from the x- coordinate of each vertex, and subtract 3 from the y-coordinate of each vertex. RuleImage A(1, 4)  A’ (1 – 5, 4 – 3)A’(–4, 1) B(4, 3)  B’ (4 – 5, 3 – 3)B’(–1, 0) C(4, –1)  C’ (4 – 5, –1 – 3)C’(–1, –4) C(1, –2)  D’ (1 – 5, –2 – 3)D’(–4, –5) B’B’ A’A’ C’C’ D’D’

Transformations 5-6 A reflection flips a figure across a line to create a mirror image.

Transformations 5-6

Transformations 5-6 Additional Example 2: Graphing Reflections on a Coordinate Plane Graph the reflection of quadrilateral ABCD across the y-axis. Multiply the x-coordinate of each vertex by –1. RuleImage A(–4, 1)  A’ (–1  –4, 1) A’(4, 1) B(–2, 1)  B’ (–1  –2, 1) B’(2, 1) C(–1, –2)  C’ (–1  –1, –2) C’(1, –2) D(–4, –3)  D’ (–1  –4, –3) D’(4, –3) A’A’ B’B’ C’C’ D’D’

Transformations 5-6 Check It Out: Example 2 Graph the reflection of triangle FGH across the x-axis. Multiply the y-coordinate of each vertex by –1. RuleImage F(–4, –2)  F’ (–4, –2  –1) F’(–4, 2) G(1, –3)  G’ (1, –3  –1) G’(1, 3) H(–2, –4)  H’ (–2, –4  –1) H’(–2, 4) H’H’ G’G’ F’F’

Transformations 5-6 A rotation turns a figure around a point, called the center of rotation.

Transformations 5-6

Transformations 5-6 Additional Example 3: Graphing Rotations on a Coordinate Plane Graph the rotation of triangle ABC 90 counterclockwise about the origin. Multiply the y-coordinate of each vertex by –1, and switch the x and y coordinates. RuleImage A(4, 4)  A’ (–1  4, 4 ) A’(–4, 4) B(4, 1)  B’ (–1  1, 4) B’(–1, 4) C(2, 1)  C’ (–1  1, 2) C’(–1, 2) A’A’B’B’ C’C’

Transformations 5-6 Check It Out: Example 3 Graph the rotation of triangle XYZ 180 about the origin. Multiply the both coordinates by –1. RuleImage X(–1, 2)  X’ (–1  –1, –1  2 ) X’(1, –2) Y(2, 3)  Y’ (–1  2, –1  3) Y’(–2, –3) Z(3, 0)  Z’ (–1  3, –1  0) Z’(–3, 0) Z’Z’ Y’Y’ X’X’

Transformations 5-6 Lesson Quiz Graph each transformation of triangle ABC. 1. translation 4 units down 2. reflection across the y-axis 3. rotation of 180 about the origin